?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Feprints.imtlucca.it%2F3114%2F&rft.title=Syncronization+and+functional+central+limit+theorems+for+interacting+reinforced+random+walks&rft.creator=Crimaldi%2C+Irene&rft.creator=Dai+Pra%2C+Paolo&rft.creator=Louis%2C+Pierre-Yves&rft.creator=Minelli%2C+Ida+G.&rft.subject=HA+Statistics&rft.subject=QA+Mathematics&rft.description=We+obtain+Central+Limit+Theorems+in+Functional+form+for+a+class+of+time-inhomogeneous+interacting+random+walks+on+the+simplex+of+probability+measures+over+a+finite+set.+Due+to+a+reinforcement+mechanism%2C+the+increments+of+the+walks+are+correlated%2C+forcing+their+convergence+to+the+same%2C+possibly+random%2C+limit.+Random+walks+of+this+form+have+been+introduced+in+the+context+of+urn+models+and+in+stochastic+approximation.+We+also+propose+an+application+to+opinion+dynamics+in+a+random+network+evolving+via+preferential+attachment.+We+study%2C+in+particular%2C+random+walks+interacting+through+a+mean-field+rule+and+compare+the+rate+they+converge+to+their+limit+with+the+rate+of+synchronization%2C+i.e.+the+rate+at+which+their+mutual+distances+converge+to+zero.+Under+certain+conditions%2C+synchronization+is+faster+than+convergence.&rft.date=2016&rft.type=Working+Paper&rft.type=NonPeerReviewed&rft.identifier=++Crimaldi%2C+Irene+and+Dai+Pra%2C+Paolo+and+Louis%2C+Pierre-Yves+and+Minelli%2C+Ida+G.++Syncronization+and+functional+central+limit+theorems+for+interacting+reinforced+random+walks.++Working+Paper+++++++(Submitted)+++&rft.relation=http%3A%2F%2Farxiv.org%2Fabs%2F1602.06217